Mathematical models have been developed to describe hormone-receptor interactions in complex cases, involving heterogeneity of hormone and/or receptor, positive and/or negative cooperativity, and failure to achieve equilibrium or steady-state conditions. Special attention has been paid to the case where either the association rate or dissociation rate constants are linear functions of receptor occupancy. Special attention is also given to the situation where the ligand is flexible and contains several functional moieties, each of which is binding to a separate subsite on the receptor area of the membrane. By use of computer simulations and curve fitting techniques, we have studied factors which affect ligand affinity, "intrinsic activity" or efficacy, and the structural requirements for the formation of full agonists, partial agonists, partial agonists/antagonists, and the distinction between competitive and noncompetitive antagonists. These models are now being applied to a variety of systems. New computer programs have been developed for estimation of affinity constants in complex systems. New techniques have been developed for the analysis of receptor-response coupling, by means of a "Logit-Logit" approach.